An FPT haplotyping algorithm on pedigrees with a small number of sites.

Doan DD, Evans PA - Algorithms Mol Biol (2011)

Bottom Line:
A computational method to infer haplotypes from genotype data is therefore important.We show that this NP-hard problem can be parametrically reduced to the Bipartization by Edge Removal problem with additional parity constraints.We solve this problem with an exact algorithm that runs in time, where n is the number of members, m is the number of sites, and k is the number of recombination events.

Affiliation: Faculty of Computer Science, University of New Brunswick, Fredericton, New Brunswick, Canada. pevans@unb.ca.

ABSTRACT

Background: Genetic disease studies investigate relationships between changes in chromosomes and genetic diseases. Single haplotypes provide useful information for these studies but extracting single haplotypes directly by biochemical methods is expensive. A computational method to infer haplotypes from genotype data is therefore important. We investigate the problem of computing the minimum number of recombination events for general pedigrees with a small number of sites for all members.

Results: We show that this NP-hard problem can be parametrically reduced to the Bipartization by Edge Removal problem with additional parity constraints. We solve this problem with an exact algorithm that runs in time, where n is the number of members, m is the number of sites, and k is the number of recombination events.

Conclusions: This algorithm infers haplotypes for a small number of sites, which can be useful for genetic disease studies to track down how changes in haplotypes such as recombinations relate to genetic disease.

Mentions:
Consider a graph G in Figure 4a where ⊕ denotes a red vertex, ∅ a green vertex, and O a grey vertex. A minimal edge bipartization set X' of size 4 illustrated by dashed lines is given in Figure 4b. We compute a mincut Y for G\X' as in Figure 4c. Set Y is the edge bipartization set of size 3 for G in Figure 4d.

Mentions:
Consider a graph G in Figure 4a where ⊕ denotes a red vertex, ∅ a green vertex, and O a grey vertex. A minimal edge bipartization set X' of size 4 illustrated by dashed lines is given in Figure 4b. We compute a mincut Y for G\X' as in Figure 4c. Set Y is the edge bipartization set of size 3 for G in Figure 4d.

Bottom Line:
A computational method to infer haplotypes from genotype data is therefore important.We show that this NP-hard problem can be parametrically reduced to the Bipartization by Edge Removal problem with additional parity constraints.We solve this problem with an exact algorithm that runs in time, where n is the number of members, m is the number of sites, and k is the number of recombination events.

Affiliation:
Faculty of Computer Science, University of New Brunswick, Fredericton, New Brunswick, Canada. pevans@unb.ca.

ABSTRACT

Background: Genetic disease studies investigate relationships between changes in chromosomes and genetic diseases. Single haplotypes provide useful information for these studies but extracting single haplotypes directly by biochemical methods is expensive. A computational method to infer haplotypes from genotype data is therefore important. We investigate the problem of computing the minimum number of recombination events for general pedigrees with a small number of sites for all members.

Results: We show that this NP-hard problem can be parametrically reduced to the Bipartization by Edge Removal problem with additional parity constraints. We solve this problem with an exact algorithm that runs in time, where n is the number of members, m is the number of sites, and k is the number of recombination events.

Conclusions: This algorithm infers haplotypes for a small number of sites, which can be useful for genetic disease studies to track down how changes in haplotypes such as recombinations relate to genetic disease.